Lyapunov-design of adaptive air-fuel ratio control for gasoline engines based on mean-value model

In order to maintain the in-cylinder air-fuel ratio (AFR) at a prescribed set point, the stoichiometric value, this paper presents an adaptive regulator of AFR control based on Lyapunov-design for the spark ignition engines. In the research, the adaptive regulator is based on the mean value model of the engine which accounts for the impingement of the injected fuel on the manifold walls and the evaporation process. Adaptive update laws are derived for estimating the uncertain parameters related to inaccuracies in air flow into the cylinders and engine torque production and the uncertain fueling parameters of the fuel injection process. The closed-loop fuel controller is realized by utilizing the information of measurable engine speed, manifold pressure and temperature, air mass flow rate through throttle and the exhaust gas oxygen (EGO) sensor at exhaust location, without knowledge of the fuel flow mass. The theoretical proof and analysis show that the closed-loop system possesses the stability and satisfactory AFR value during both steady state and transient operation. Moreover, simulation on an engine test bench demonstrates the capability of the adaptive controller to recover the performance and robustness properties of the control system in the case of uncertainty, disturbance and the intake-to-power delay and the measurement delay of the oxygen sensor.